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dielectric.c
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#ifndef lint
static const char RCSid[] = "$Id: dielectric.c,v 2.30 2019/04/19 19:01:32 greg Exp $";
#endif
/*
* dielectric.c - shading function for transparent materials.
*/
#include "copyright.h"
#include "ray.h"
#include "otypes.h"
#include "rtotypes.h"
#include "pmapmat.h"
#ifdef DISPERSE
#include "source.h"
static int disperse(OBJREC *m,RAY *r,FVECT vt,double tr,COLOR cet,COLOR abt);
static int lambda(OBJREC *m, FVECT v2, FVECT dv, FVECT lr);
#endif
static double mylog(double x);
/*
* Explicit calculations for Fresnel's equation are performed,
* but only one square root computation is necessary.
* The index of refraction is given as a Hartmann equation
* with lambda0 equal to zero. If the slope of Hartmann's
* equation is non-zero, the material disperses light upon
* refraction. This condition is examined on rays traced to
* light sources. If a ray is exiting a dielectric material, we
* check the sources to see if any would cause bright color to be
* directed to the viewer due to dispersion. This gives colorful
* sparkle to crystals, etc. (Only if DISPERSE is defined!)
*
* Arguments for MAT_DIELECTRIC are:
* red grn blu rndx Hartmann
*
* Arguments for MAT_INTERFACE are:
* red1 grn1 blu1 rndx1 red2 grn2 blu2 rndx2
*
* The primaries are material transmission per unit length.
* MAT_INTERFACE uses dielectric1 for inside and dielectric2 for
* outside.
*/
#define MLAMBDA 500 /* mean lambda */
#define MAXLAMBDA 779 /* maximum lambda */
#define MINLAMBDA 380 /* minimum lambda */
#define MINCOS 0.997 /* minimum dot product for dispersion */
static double
mylog( /* special log for extinction coefficients */
double x
)
{
if (x < 1e-40)
return(-100.);
if (x >= 1.)
return(0.);
return(log(x));
}
int
m_dielectric( /* color a ray which hit a dielectric interface */
OBJREC *m,
RAY *r
)
{
double cos1, cos2, nratio;
COLOR ctrans;
COLOR talb;
int hastexture;
int flatsurface;
double refl, trans;
FVECT dnorm;
double d1, d2;
RAY p;
int i;
/* PMAP: skip refracted shadow or ambient ray if accounted for in
photon map */
if (shadowRayInPmap(r) || ambRayInPmap(r))
return(1);
if (m->oargs.nfargs != (m->otype==MAT_DIELECTRIC ? 5 : 8))
objerror(m, USER, "bad arguments");
raytexture(r, m->omod); /* get modifiers */
if ( (hastexture = DOT(r->pert,r->pert) > FTINY*FTINY) )
cos1 = raynormal(dnorm, r); /* perturb normal */
else {
VCOPY(dnorm, r->ron);
cos1 = r->rod;
}
flatsurface = r->ro != NULL && isflat(r->ro->otype) &&
!hastexture | (r->crtype & AMBIENT);
/* index of refraction */
if (m->otype == MAT_DIELECTRIC)
nratio = m->oargs.farg[3] + m->oargs.farg[4]/MLAMBDA;
else
nratio = m->oargs.farg[3] / m->oargs.farg[7];
if (cos1 < 0.0) { /* inside */
hastexture = -hastexture;
cos1 = -cos1;
dnorm[0] = -dnorm[0];
dnorm[1] = -dnorm[1];
dnorm[2] = -dnorm[2];
setcolor(r->cext, -mylog(m->oargs.farg[0]*colval(r->pcol,RED)),
-mylog(m->oargs.farg[1]*colval(r->pcol,GRN)),
-mylog(m->oargs.farg[2]*colval(r->pcol,BLU)));
setcolor(r->albedo, 0., 0., 0.);
r->gecc = 0.;
if (m->otype == MAT_INTERFACE) {
setcolor(ctrans,
-mylog(m->oargs.farg[4]*colval(r->pcol,RED)),
-mylog(m->oargs.farg[5]*colval(r->pcol,GRN)),
-mylog(m->oargs.farg[6]*colval(r->pcol,BLU)));
setcolor(talb, 0., 0., 0.);
} else {
copycolor(ctrans, cextinction);
copycolor(talb, salbedo);
}
} else { /* outside */
nratio = 1.0 / nratio;
setcolor(ctrans, -mylog(m->oargs.farg[0]*colval(r->pcol,RED)),
-mylog(m->oargs.farg[1]*colval(r->pcol,GRN)),
-mylog(m->oargs.farg[2]*colval(r->pcol,BLU)));
setcolor(talb, 0., 0., 0.);
if (m->otype == MAT_INTERFACE) {
setcolor(r->cext,
-mylog(m->oargs.farg[4]*colval(r->pcol,RED)),
-mylog(m->oargs.farg[5]*colval(r->pcol,GRN)),
-mylog(m->oargs.farg[6]*colval(r->pcol,BLU)));
setcolor(r->albedo, 0., 0., 0.);
r->gecc = 0.;
}
}
d2 = 1.0 - nratio*nratio*(1.0 - cos1*cos1); /* compute cos theta2 */
if (d2 < FTINY) /* total reflection */
refl = 1.0;
else { /* refraction occurs */
/* compute Fresnel's equations */
cos2 = sqrt(d2);
d1 = cos1;
d2 = nratio*cos2;
d1 = (d1 - d2) / (d1 + d2);
refl = d1 * d1;
d1 = 1.0 / cos1;
d2 = nratio / cos2;
d1 = (d1 - d2) / (d1 + d2);
refl += d1 * d1;
refl *= 0.5;
trans = 1.0 - refl;
trans *= nratio*nratio; /* solid angle ratio */
setcolor(p.rcoef, trans, trans, trans);
if (rayorigin(&p, REFRACTED, r, p.rcoef) == 0) {
/* compute refracted ray */
d1 = nratio*cos1 - cos2;
for (i = 0; i < 3; i++)
p.rdir[i] = nratio*r->rdir[i] + d1*dnorm[i];
/* accidental reflection? */
if (hastexture &&
DOT(p.rdir,r->ron)*hastexture >= -FTINY) {
d1 *= (double)hastexture;
for (i = 0; i < 3; i++) /* ignore texture */
p.rdir[i] = nratio*r->rdir[i] +
d1*r->ron[i];
normalize(p.rdir); /* not exact */
} else
checknorm(p.rdir);
#ifdef DISPERSE
if (m->otype != MAT_DIELECTRIC
|| r->rod > 0.0
|| r->crtype & SHADOW
|| !directvis
|| m->oargs.farg[4] == 0.0
|| !disperse(m, r, p.rdir,
trans, ctrans, talb))
#endif
{
copycolor(p.cext, ctrans);
copycolor(p.albedo, talb);
rayvalue(&p);
multcolor(p.rcol, p.rcoef);
addcolor(r->rcol, p.rcol);
/* virtual distance */
if (flatsurface ||
(1.-FTINY <= nratio) &
(nratio <= 1.+FTINY))
r->rxt = r->rot + raydistance(&p);
}
}
}
setcolor(p.rcoef, refl, refl, refl);
if (!(r->crtype & SHADOW) &&
rayorigin(&p, REFLECTED, r, p.rcoef) == 0) {
/* compute reflected ray */
VSUM(p.rdir, r->rdir, dnorm, 2.*cos1);
/* accidental penetration? */
if (hastexture && DOT(p.rdir,r->ron)*hastexture <= FTINY)
VSUM(p.rdir, r->rdir, r->ron, 2.*r->rod);
checknorm(p.rdir);
rayvalue(&p); /* reflected ray value */
multcolor(p.rcol, p.rcoef); /* color contribution */
copycolor(r->mcol, p.rcol);
addcolor(r->rcol, p.rcol);
/* virtual distance */
r->rmt = r->rot;
if (flatsurface)
r->rmt += raydistance(&p);
}
/* rayvalue() computes absorption */
return(1);
}
#ifdef DISPERSE
static int
disperse( /* check light sources for dispersion */
OBJREC *m,
RAY *r,
FVECT vt,
double tr,
COLOR cet,
COLOR abt
)
{
RAY sray;
const RAY *entray;
FVECT v1, v2, n1, n2;
FVECT dv, v2Xdv;
double v2Xdvv2Xdv;
int success = 0;
SRCINDEX si;
FVECT vtmp1, vtmp2;
double dtmp1, dtmp2;
int l1, l2;
COLOR ctmp;
int i;
/*
* This routine computes dispersion to the first order using
* the following assumptions:
*
* 1) The dependency of the index of refraction on wavelength
* is approximated by Hartmann's equation with lambda0
* equal to zero.
* 2) The entry and exit locations are constant with respect
* to dispersion.
*
* The second assumption permits us to model dispersion without
* having to sample refracted directions. We assume that the
* geometry inside the material is constant, and concern ourselves
* only with the relationship between the entering and exiting ray.
* We compute the first derivatives of the entering and exiting
* refraction with respect to the index of refraction. This
* is then used in a first order Taylor series to determine the
* index of refraction necessary to send the exiting ray to each
* light source.
* If an exiting ray hits a light source within the refraction
* boundaries, we sum all the frequencies over the disc of the
* light source to determine the resulting color. A smaller light
* source will therefore exhibit a sharper spectrum.
*/
if (!(r->crtype & REFRACTED)) { /* ray started in material */
VCOPY(v1, r->rdir);
n1[0] = -r->rdir[0]; n1[1] = -r->rdir[1]; n1[2] = -r->rdir[2];
} else {
/* find entry point */
for (entray = r; entray->rtype != REFRACTED;
entray = entray->parent)
;
entray = entray->parent;
if (entray->crtype & REFRACTED) /* too difficult */
return(0);
VCOPY(v1, entray->rdir);
VCOPY(n1, entray->ron);
}
VCOPY(v2, vt); /* exiting ray */
VCOPY(n2, r->ron);
/* first order dispersion approx. */
dtmp1 = 1./DOT(n1, v1);
dtmp2 = 1./DOT(n2, v2);
for (i = 0; i < 3; i++)
dv[i] = v1[i] + v2[i] - n1[i]*dtmp1 - n2[i]*dtmp2;
if (DOT(dv, dv) <= FTINY) /* null effect */
return(0);
/* compute plane normal */
fcross(v2Xdv, v2, dv);
v2Xdvv2Xdv = DOT(v2Xdv, v2Xdv);
/* check sources */
initsrcindex(&si);
while (srcray(&sray, r, &si)) {
if (DOT(sray.rdir, v2) < MINCOS)
continue; /* bad source */
/* adjust source ray */
dtmp1 = DOT(v2Xdv, sray.rdir) / v2Xdvv2Xdv;
sray.rdir[0] -= dtmp1 * v2Xdv[0];
sray.rdir[1] -= dtmp1 * v2Xdv[1];
sray.rdir[2] -= dtmp1 * v2Xdv[2];
l1 = lambda(m, v2, dv, sray.rdir); /* mean lambda */
if (l1 > MAXLAMBDA || l1 < MINLAMBDA) /* not visible */
continue;
/* trace source ray */
copycolor(sray.cext, cet);
copycolor(sray.albedo, abt);
normalize(sray.rdir);
rayvalue(&sray);
if (bright(sray.rcol) <= FTINY) /* missed it */
continue;
/*
* Compute spectral sum over diameter of source.
* First find directions for rays going to opposite
* sides of source, then compute wavelengths for each.
*/
fcross(vtmp1, v2Xdv, sray.rdir);
dtmp1 = sqrt(si.dom / v2Xdvv2Xdv / PI);
/* compute first ray */
VSUM(vtmp2, sray.rdir, vtmp1, dtmp1);
l1 = lambda(m, v2, dv, vtmp2); /* first lambda */
if (l1 < 0)
continue;
/* compute second ray */
VSUM(vtmp2, sray.rdir, vtmp1, -dtmp1);
l2 = lambda(m, v2, dv, vtmp2); /* second lambda */
if (l2 < 0)
continue;
/* compute color from spectrum */
if (l1 < l2)
spec_rgb(ctmp, l1, l2);
else
spec_rgb(ctmp, l2, l1);
multcolor(ctmp, sray.rcol);
scalecolor(ctmp, tr);
addcolor(r->rcol, ctmp);
success++;
}
return(success);
}
static int
lambda( /* compute lambda for material */
OBJREC *m,
FVECT v2,
FVECT dv,
FVECT lr
)
{
FVECT lrXdv, v2Xlr;
double dtmp, denom;
int i;
fcross(lrXdv, lr, dv);
for (i = 0; i < 3; i++)
if ((lrXdv[i] > FTINY) | (lrXdv[i] < -FTINY))
break;
if (i >= 3)
return(-1);
fcross(v2Xlr, v2, lr);
dtmp = m->oargs.farg[4] / MLAMBDA;
denom = dtmp + v2Xlr[i]/lrXdv[i] * (m->oargs.farg[3] + dtmp);
if (denom < FTINY)
return(-1);
return(m->oargs.farg[4] / denom);
}
#endif /* DISPERSE */
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